Notes For Bachelor of Science (TU)

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1 Introduction
1.1 Computer

Basically it is a fast caleulating machine which is now a days nsed for variety of uses
ranging from house hold works to space technology. The credit of invention of this
machine goes to the
English Mathematician Charles Babbage.
1.2 Types of Computer
Based on nature, computers classified
into Analog computers and
are
Digital computers.
The former one deals with measuring physical quantiies (concerned with continuous
variables) which are of late rarely used. The digital computer operates by counting and
it deals with the discrete
variables. There is a combined form called Hybrid computer,
which has both features.

Based on application computers are classified as special purpose computers and gen-
eral computers. As the name tells special computers are designed to performn certain
specifie tasks where as the other category is designed to cater the needs of rariety of
lusers.

1.3 Basic Structure of a Digital Computer

he vou Nemann architect ure, whicl1 is also knoWn as the von Neumann niodel and
Princeton architecture, is a computer architectunre based on that described in 1945 by the
mathenatician and physicist John von Neumamn.This describes a design architectre
for an electronic digital computer with parts cousisting of a processing unit containing
an arithetic logic unit and processor registers; a control unit containing an instruction
register and program counter; a memory to store both data and instructious; cxternal
mass storage: ad input and output mechanisms.The key idea of the Vou Neumam a-
chitect ure is the stored program concept.A store-progran digital couputer is oue that
keeps its program instructions, as well as its data. in read-write, randonm-access nenory
(RAM). Storec-program computers were an advancemet over the program-cotrolled
computers of the 1940s.

Central Processing Unit

Control Unit

Input Output
Device Arithmetic/logic Unit| Devce

Memory Unit

Figure 1: Block Diagram of Computer

The ma conponents of a conmputer are lnput unit (1U), Central Processing nit (CPU)
ad Output mit (OU). The inlormation like data. prograns ete are passed to the com-
puter through input devices. The keyboard. mouse, Iloppr disk. CD. DVD. joyst ick etc
 from à colpter
out put device is to get information
t a m input devices. "The
disk, CD etc
are otplut
Printer, Ploppy
DIOCeSsing .
VDU (Visual DisDlay Unit),
devices.
components- Memory unit, unit Control

O a computer is CPU. It has three unit also called storage

device 1s to
Memory
c etic and Logical unit (ALU)- there in computer. They are RAM (ran-
are a called, it 1s
i . Two types menory When a program is
emory) and ROM (read only memory). wlat e v e r stored
sd When the conmputer
is Switched oft,
PLOCessed in RAM. Where as ROM 1s a pe1mallent
A M will be deleted.So it is a teuporary memory.
Inside a computer there
stored for future
use.
ry, where data, program etC are time.
stored and can be accessed at any
E e aevice called Hard disk, where data are

of instructions stored
The O r o l luit is for controlling the execution and interpreting
arithmetic and logical operations are pe-
e
nemory. ALU is the mit where the of binary digits, called
transformed to groups
h e infomation to a computer is
edl from 8 to 64. A group of 8
computer,
varies from computer to
O hee length of bit one alphanumeric (
Alphabets and
1 s Called a Byte and a byte generally
represents
are called hardwares.
But
of a computer
Nnerals) character. The physical components A set of instructios 1s called
a
lOr the nachine to work it requires certain progran1s (

softwares. There are two types of

softwares System soft- -

prOgram ). They are called

ware and Application software System software includes Operating systems, Utility

prograns and Language processors.

1.3.1 Operating System

The set of instructions which resides in the computer and governs the system are called
the medium
function. They
operating systems, without which the machine will never are

of communication between a computer and the user. DOS, Windows, Linux, Unix etc
are Operating Systems.

1.3.2 Utility Programs

These programs are developed by the manufacturer for the users to do various tasks.
Word, Excel, Photoshop, Paint etc are some of them.

1.4 Programming Language

1.4.1 Low level Languagge
Low level languages are machine level and assembly level language. In machine level
language computer only understand digital numbers i.e. in the form of 0 and 1. So,
instruction given to the computer is in the form binary digit, which is difficult to im-
plement instruct ion in binary code. This type of program is not portable, difficult to
maintain and also error prone. The assembly language is on other hand modified version
of machine level language. Where instructions are given in English like word as ADD,
SUM, MIOV etc. It is easy to write and understand but it is hard for the computer to
understand. So the translator used here is assembler to translate into machine level.
Although language is bit easier, programmer has to know low level details related to
low level language. ln the assembly level language the data are stored in the computer
register. which varies for different computer. Hence it is not
portable.
1.4.2 High level Language
These languages are machine independent, means it is portable. The language in this
category is Pascal, Cobol, Fortran etc. High level languages are not understood by the
machine. So it needs to translate by the translator into machine level. A translator is
Software which is used to translate high level language as well as low level language in
to machine level language.

1.5 Compiler, Interpreter and Assembler

Compiler and interpreter are used to convert the high level language into machine level
language. The program written in high level language is known as source program and
the corresponding machine level language program is called as object program. Both
compiler and interpreter perform the same task but there working is different. Compiler
read the program at-a-time and searches the error and lists them. If the program is error
free then it is coverted into object program. When program size is large then compiler
is preferred. Whereas interpreter read only one line of the source code and covert it to
object code. If it check error, statement by statement and hence of take more time.

An assembler program creates object code by translating combinations of mnemonics

and syntax for operations and addressing modes into their numerical equivalents. This
representation typically includes an operation code ("opcode") as well as other control
bits and data. The assembler also calculates constant expressions and resolves symbolic
1ames for memory locations and other entities.

1.6 Traditional and Structured Programming

Structured programming is a programming paradigm aimed at improving the clarity,
quality, and development time of a computer program by making extensive iuse of sub-
routines, block structures, for and while loops-in contrast to using simple tests and
jumps such as the go to statement which could lead to "spaghetti code" causing diffi-
culty to both follow and maintain.

It is possible to do structured programming in any programming language, though it

is preferable to use something like a procedural programming language. Some of the
langiiages initially used for structured programming include: ALGOL, Pascal. PL/I and
Ada but nost new prorcdural programming languages sinee that time have inchuded
features to encourage structured programming, and sometimes deliberately left ont fea-
tures notably GOTO - in an effort to make unstructured programning more dificnlt,
Structured programming (somefimes known as mocdular programming) i a subset of
imperative programming that enforces a logical structure on the program being Written
to make it more cffhicicnt and easier to understand and modify.
 2 Programming Logic
Problems solving

First and foremost step of solving a problem is knowing about the nature of problem in
order to solve it. Almost all types of problems can be solved with computer. However,
correct fornmulation of the problem in computer understandable terms is essential to
formulate the problem and solve it using computer.

2.1 Understanding of problems, Feasibility and Requirement Analysis

In order to start to develop a solution to a problem using computer, we need to first
understand the problem about its nature, complexities and others. Problems can be of
various natiire and we need to understand about the problems first to be able to solve
it using computer. Once the problem has been understood and we can solve it using
computer the feasibility of the problem solution needs to be determined. We can solve a
problem using varions logic but what needs to be worked out is the most feasible solut ion
that can be derived with the least amount of complexities. Anot her major portion t
solving problems using computer is the analysis of the requiremcnts. The solution to
the problem can be solved however the requirements required is beyond the posSSI DIC

technologies of today. Then the solution may not be feasible to the problem.

2.2 Design FlowChart and Algorithm

An algorithm is a solution to a computer programning problem. In other words a step

be
by step procedure for developing a problem is called an algorithm.Algorithns can

written in two different ways

is an ar-
1. Pseudocode English like steps that describe the solution.Pseudocode
hms. Pseu-
tificial and informal language that helps programmers develop algorit
docode is a "text-based" detail (algorithmic) design tool.The rules of Pseudocode
are to be
are reasonably straightforward. All statements showing dependency"
indented. These include while, do, for, if, switch.
Set total to zero
Set grade counter to one
is less than or equal to ten
counter
While grade
Iuput the next grade
into the total
Add the grade
Set the class average to the total. divided by ten

Print the class average

blocks detailing out the logical flow

2. FlowChart Pictures Detailing with specific
it is represented
of the solution. better understanding of an algorithm,
For a

representation of an algorithm is called a Flow Chart.

pictorially.The pictorial
and flowchart to add two umbers can be stated as:
The algorithm

numbers as a and b
(a) Stepl: Input
(b) Step2: Sum = x +y

(c) Step3: Print the sum

Varous symbols can be used to represent ditterent actions like taking input, making

decisions and connecting flowelharts.

10
 Symbol Name Function

stort/end

. Iiitsiit%}

Figure 2: Flow chart Basic Symbols

The flow chart for tlhe addition of two numbers whose algorithm has becn stated above
can be drawn as

2.3 Program Coding

Once algorithm and fHowchart has been developed the task now remains is to write
programs using some high level programming language.C, C++, Java. Python are the
most popular programming language to develop programs. PHP and ASP remain a
popular choice for developing web based applications.

2.4 Testing and Debugging

Once the program code has been written in a selected program1ning language of choice
the next task to complete is the testing and debugging. Testing and debugging helps
to find the problems associat ed with the program behavior under normal and abnormal
circumst ances. Extensive testing like white box testing and black box testing, integration
testing needs to done before the program is deployed into the real world scenario.

2.5 Implementation
After a program has been Written and tested it necds to be implemented to the target
environmcnt to solve the problem. Various necds of physical hardware and accessories
rcqnired by the program to solve the intended problem necds to be present upon implo-
mcntation. Once the program is implemcnted it starts to work.
2.6 Evaluation and Maintenance
The evaluation of the performance of the program needs to be done at frequent interval
once the program or software is implemented. The advent of new technology, upscaling
and downscaling of the business, request for the change from customers, finding ofa
new bug are the major reasons for the maintenance and change of the softwares. Once
changes have been continuous monitoring of the software perfornance needs to done to
discover the flaws in the software.

2.7 Documentation
The same workforce that developed the program may have left the project and gone in
search of opportunities. So a program must be well documented in order for the new
people to understand how the software was developed and how can it be modified. The
documentation start from the very beginning of the problem formulation to the very
end of the Evaluation and Maintenance.
3 Variables and Data Types
3.1 Constant and Variables
The smallest meaningful units in C programming is called C Token. Keywords. vari-
ables. various special characters fall nder c tokens.

Const ants refer to fixed values that the program may not alter during its execution.
These fixed values are also called literals. Constants can be of any of the basic data
types like an integer const ant, a floating constant, a character constant, or a string
literal. There are enumeration constants as well.Constants are treated just like regilar
variables except that their values cannot be modified after their definition.

variable is nothing but a name given to a storage area that our programs can ma
nipulate. Each variable in C has a sperific type, which determines the size and layout
of the variable's memory: the range of values that can be stored within that memory:
and the set of operations that can be applied to the variable.The name of a variable
can be composed of letters, digits, and the underscore character. It must begin with
either a letfer or an underscore. Upper and lowercase letters are distinct because (C15

case-sensitive.

Type Size(Byte) Range

char 127 to 127
int 2 -32,767 to 32,767
Hoat 1*10-37 to 1*103 six
digit precision
double 8 110-3 to 1*1037 ten
digit precision
long int -2,147,483,647 to

2.147,483.647

Table 1: Data types in C

3.2 Variable declaration in C

A variable declaration provides assurance to the compiler that there exists a variable
with the given typc and name so that the compiler can proccod for further compilat ion
without requiring the complete detail about the variable. A variable definition has its
meaning at the time of compilation only, the compiler needs actual variable dcfinit ion
at the time of linking the program.

#include <stdio.h>
extern int a. b:
exter 1nt C:

extern float I:
iut mai1 ()
int a, b:
iut c:
Iloat f:

=10

b = 20:

3
 c
valne
ol
printl(
\u 1)
70.0/3.0
f:
%l
value of
printi(

Ieturn 0

name
in C

writing
variable
and
lowercase
ers), digits
letters)

Rules for ippercase

3.3 letters (both

have
can
name

I. A
variable
Ho
and underscore only letter or an
underscore.
ever,
either a

variable
should be
u d e r s c o r e .
It is because
vari
uiable
of a With a l and
The first letter variable
name
à system name d 1lay
2. with
to start can
colilct

discouraged
it is an
underscore

starts
with
name
that

cause error. the first 31 charact.

ters
However,
variable c a n be. irst 31 letters of two
rule on how long a
bo, the
3. There is
no the compiler.
are
discriminated by
variable
of a
should be different.

in a program
variables

Function
3.4 Input Output to read given input
built-in functions
many of the
language provides
C programming
screen, printer or in any file.
and write data on

functions
scanf () and printf()

#include <st dio h> .

#include <conio h> .

void main ()

int i:
printf( Enter a value")
scanf("d",&i );
printf\nYou entered: d " ,i );
getch ():

3.5 Operators in C
An operator is a symbol that tells the compiler to perform specific mathematica r
logical functions. C
Janguage is rich in built-in operators and provides the
ypes of perators. followl
Arithnet ic Operator
Relational Operator
.Logical Operator
.Bitwise Operator
A ent )erator
Mise (Operalor
3.5.1 Arithmetic Operator
The basic operators for performing arithmetic are the same in many computer languages:

1. + Addition
2. -

Subtraction
*
3. Multiplication
4. Division

5. Modulus (Remainder)
The order of precedence of these
For exponentiations we use the library function pow.
operators is % /* + - . it can be overruled by parenthesis.

Division of an integer quantity by another is referred to integer division. This operation

results in truncation. i.e.\When applied to integers, the division operator/ discards any
remainder, so 1/ 2 is 0 and 7/4 is 1. But when either operand is a floating-point
a fioating-point result,
with
quantity (type float
or double the
), division operator yields
and 7.0/4.0 is 1.75.
a potentially nonzero fractional part. So 1/2.0 is 0.5,
to produce a new value is called a unary
A operator acts up on a single operand
++ and - are unary operators.
operator. The decrement and increment operators
-

increase and decrease the value by 1.

They
The output given by the sizeof() operator de-
sizeof() is another unary operator.
The values stated by sizeof() operator down below
pends on the computer architecture.
are based on a 16 bit compile.

i n t X, Y
2 =sizeof(x )
of integer type data is 2 that of float is 4, that of
The value of y is 2. The sizeof() an

double is 8. that of char is 1.

3.5.2 Relational Operator

than
than or cqual (greater than ), >= ( grcater
to ), >
<less than ), <= (less A
to ) are relational operators.
( cqual to ) and! (not cqual
=

or cqual to ).
==

with a relational operator.

For example "b*b
connected
logical cxpression is expression
expression. Its value is cither true or false.
-4*a*c<0 is a logical

i n t i j ,k:
2 i=l:

3 j=2:
=i+)
the expression k<5 evaluates to true.
The expression k>5 evaluates to lalse and

3.5.3 Logical Operator

with arbitrary numbers and gencrate
true/false values. You
work
The rclational opcrators take true/false
values by iusing the Boolran operators, which
can also combine truc/false are:
new true/talse
valucs. The three Boolean operators
values as operands and compute

1. && AND
 2. OR
3. ! NOTT

values and produces

true/false
takes two
( a n d ' ")
operator
(that is, if the l e f t -
The && operands a r e
true
(1) result it both
The |I ( o r ' ')
a true side is true).
true and the right-hand result
side is a true (1)
hand true/false values and produces
two
operator
takes
operator
takes a single
1s t r u e . The! ('not' ' )
operand and t r u e to
if either turning
false to true
v a l u e and negates it,
true/false
and nonzero to 0).
false (O to l
connect logical expressions.
used to
operators which
are
and || (or) are logical
&& (and ) expression.
( not) 1S unary operator,
acts on a single logical
Where as!
(a<5) && (a>2)
2 (a<=3) | (a>2) returns true.
it a= 3 or a=6 the logical expression
In the example

3.5.4 Assignment Operator

identiier.
to another
a value of expression
are used tor assigning
These operators

and % are assignnent operators.

/=
=
=,

the value of b-+c in 'a'.

= btc results storing the value of a by 5.
a
in

a + = 5 results
in increasing a=a/3
in a and it is cquivalent
results in storing the value a/3
a/=3

3.5.5 Conditiomal Operator

variable 1 = expression ?
It is used as

operator ?: is the conditional operator. and expression 2

The 1 is a logical expression
expression 3. Here expression 1 is truc, value
expression 2: numerical values. If expression
expressions having
and expression 3
are
otherwise expression3
is assigned.
to variable 1 and
of expression 2 is assigned

i n t a,b,c,d,e;:
2 a=3; b=5; c=8;
? a b;
3 d=(a<b)
4e=(b>c) ? b C

3 and e =
8.
results the value of d
=

The evaluation of the expression

3.5.6 Bitwise Operator

known as bitwise oprator
for manip-
operator
Chas a distinction of supporting special bits or shifting them
are used for testing
ulation of data at bit level.
These operators
or double. Following
arc the
not be applied to float
ight or left. Bitwise operator may
bitwise operators.

bitwise AND

bitwise OR

bitwise cxclusive OR

shift left

slilt riglht
 3.6 Operator Precedence in C
Operator precedence determines the grouping of terms in an expression and decides how
an expression is evaluated. Certain operators have higher precedence than others; for

example, the multiplication operator has higher precedence than the addition
a
operator
oexample, x = 7+3* 2; here, x is assigned 13, not 20 b e c a u s e o p e r a t o r * has

a higher precedence than +, so it first gets multiplied with 3*2 and then adds into 7.An

arithmetic expression without parenthesis will be evaluated from left to right using the
Tules of precedence. There are two distinct priority levels of arithmetic operators in C.

.Higher Priority */
.Lower Priority +
The expression x=a-b/3+c*2-1 where a=9, b=12 and c=3 will be evaluated as
stepl: x=9-12/3+3*2-1 Higher priority operators left to right division first
step2: x=9-4+3*2-1 Higher priority operators left to right multiply
step3: x=9-4+6-1 Lower priority operators left to right subtraction
step4: x=5+6-1 Lower priority operators left to right additio
step5: x=11-1 Lower priority operators left to right subtraction
step6: x=10 Final Result

Rules for Evaluation of Expression

right evaluated.
First, parenthcsized sub expression from left to arc

I f parentheses are nested, the evaluation begins with innermost sub expression.

T h e precedence rule is applied in determining the order of operands in evaluating

sub expressions.
Arithmetic expressions are evaluated from left to right using the rules of prece-

dence.
When parentheses are used. the expressions within the parent heses assume highest

priority.

Function
3.7 Simple Input Output
func-
data we use library function .the important of these
For inputting and outputting
gets( ), puts().
tions are getch( ). putchar( ), scanf( ), printf( ),
3.7.1 getchar() function
is
It is used to read a (char type) from keyboard. The syntax
single character
char variable name = getchar( ;
For reading an array of character's or a string we can use getchar( ) functio

#include<st dio .h>

2 #include<conio . h>
svoid main )

5char place 80:

,i1nt i:
++i):
7 for ( i = 0:( place i = g e t c h a r) ) = ' \ n ,

17
 3.7.2 putchar() function
is
It is used to display single character. The syntax
putchar(char c);

#include <stdio.h>
2 #include <conio.h>
3 void main ()

s char alphabet
6 printf(*Enter-an.alphabet):
putchar '\n ');
8 alphabet=getchar ();
9 putchar (alphabet ) ;
10

3.7.3 scanf() function

This function is generally used to read any data type- int, char, double. fHoat,string. The
syntax is
scanf (control string, list of arguments)
and a

The control string consists of group of

characters, each group beginning % sign
the data of the data item. The conversion characters
conversion character indicating type
floating point value in
are c.d.e.i,o,5, u,x indicating the type resp.
char decimal integer,
unsigned
form, floating point value with decimal point, octal integer, string,
exponent characters.
ie, "%s", "%d" etc are such group of
integer, hexadecimal integer.
#include<st dio.h>
2 #include<conio.h>
3 void main(

5 char name |30], line

6 int x;
7 float y;

10 Scanf"%s%d%T, name, &x, ky);

11 Scanf ( "%c" , 1ine ):
12

3.7.4 printf() function

used function for outputting a data of any type. The syntax

This is the most commonly
is
list of arguments)
printf(control string,
control string consists of group of characters, each group having % symbol
Here also
conversion characters like c, d, o, f, x etc.
and

#include<st dio .
h>
2 #include<conio .h>
3 void main ()

5 int X
6Scanf"%d",&x);

7 X=X * X ;

print f(Thesquare0l ~thelumberis-d" , x):

9

I8
Note that in this list of arguments the variable names are without & symbol unlike inn
the case of scanf() function. In the conversion string one can include the message to

displayed and is
be displayed. In the above example "The square of the number is" is
followed by the value of x.

3.7.5 gets() and puts() function

reads a line from stdin and
stores it into the string pointed
The C library function gets()
read or when the
end-of-file is
newline character is
to by str. It stops when either the
reached, whichever comes first.

##include<stdio .h>
2 #include<conio .h>
3 int main ()

s char str |50]:

6 printf(" Enter-a-string-:);
78ets(str);
8printt(You.entered:%s, str):
9 return (0)
10

to stdout up to but
not including the
function int puts() writes a string
The C library to the output.
null character. A newline character is appended

#include <stdio.h>
.h>
2 #include <string
3 int main ()

5 char strl |15;

6 char str2|l5;
"Nepal" ):
7 strePy ( strl, Online" );
8strepy(str2 ,

9puts(strl );
10 puts ( str2):
11 return (0);
12

19
 4 Control Statements in C

C provides two types of Control Statements

Branching Structure
Looping Structure
4.1 Branching Structure

Branching is deciding what actions to take and looping is deciding how many times to
take a certain action.Decision making structures
require that the programmer specifies
one or more conditions to be evaluated or tested by the program, along with a statement
or statenments to be executed if the condition is determined to be
true, and optionally,
other statements to be executed if the condition is determined to be false. Show below is
the general form of a typical decision
making structure found in most of the programming
languages.

conditlon

fiscondition|
true
fs condition
false

conditional
code

Figure 3: FlowChart Control Statement

4.1.1 if Statement

An if statement consists of a Boolean expression followed by one or more statements.If

the Boolean expression evaluates to true, then the block of code inside the 'if' statement
will be executed. If the Boolean expression evaluates to false, then the first set of code
after the end of the if' statement (after the closing curly brace) will be executed. C
programming language assumes any non-zero and non-null valnes as true and if it is
either zero or null, then it is assumed as false value.

#include <stdio .h>

2 i n t main ()
int a = 10:

if a < 20
printf(auis~less ~than20\n" )
printfvalue ol -a 1S~ d\n", a );
return 0;

20
 If condition
true
condition

H condition conditfonal code

is false

Figure 4: if statement flowchart

4.1.2 if..else Statement

the
optional else statement, which executes when
An if statement can be followedby an

Boolean expression evaluates to true, then the if block

Boolean expression is false.If the
language
vill be executed,otherwise, tlhe else block will be executed.C programming
null, then it
a s s u m e s any n o n - z e r o and
non-null values as true,and if it is either zero or

is assumed as false value.

If condition
IS true

conditon

If condition if code
is false

else code

Figure 5: If else Statement

#include <stdio .h>

int main () 1
int a = 100:

if( a = 10)
printf"Valucofauis10\n );

else if( a = 20 1
printfValueof-auis~20 n ) :

else if( a == 30)

printf(" Valueol-a.isu30|n);

13 else
21
 PrinttNoneofthe.ValuesisnaLehing\

Exactvalue~ofa-is : d\n"
,
)
printt
17 return 0;

4.1.3 if..else if.else Statement

which is very
An it statement can be followed by an optional clse if...else statement,
using if...else
1scful to test various conditions using single if..else if statement.When
if...clse statements, there are few points to keep in mind:
else's and it must come after any else if's.
An if can have zero or one

else if's and they must come betore the else.

have to many
An if can zero

of the remaining elsc if's or clse's will be tested.

Once an else if succeeds, none

4.1.4 Nested if Statement

can use
It is always legal in C programming to nest if-else statements, which means you
one if or else if statement inside another if or else if statement(s).

4.1.5 Switch Statement

of values.
A switch statement allows variable to be tested for equality against a list
a
switched on is checked for each switch
Each value is called a case, and the variable being
case.The following rules apply to a switch statement:

enumerated
must have an integral or
T h e expression used in a switch statement
has a single conversion
function to
of class type in which the class
type, or be a

an integral or eumerated type.

statements within a switch. Each case is followed

You can have any number of case
colon.
the value to be compared to and a
by
must be the same data type as the variable in
T h e constant-expression for a case
const ant or a literal.
the switch, and it must be a
.When the variable being switched on is equal to a case, the statements following

will execute until a break statement is reached.

that case

.When a brcak statement is reached, the switch terminates, and the flow of control

jumps to tlhe next line follOwing the switch statement.

Not every case needs to contain a break. lf no break appears, the fow of control
to subsequent cases until a break is reached.
will fall through
. A switch stateinent can have an optional dletault case, which must appear at the
end of the switch. The default case can be used for performing a task when none
of the cases is true. No break is needed in the default case.

# i n c l u d e <stdio.h>

i n tmain ()
/ local variable definition */
char grade = B

switch( grade)
22
 expresslon

Case code block 1

case 2 code block2

Caso 3
cOde block 3

detauir code block N

Figure 6: switch statement flowchart

case A :
printf(t Excellent !\n" ):
break;
case B
case C
printf( Welldone\n" );
break
case DD
4
printf("You passed \n" ):
break;
case'F

printf( Bettertry~again \n
18 break;
9
default
printf(Invalid grade \n" );

printf("Your-grade-is - c \ n , grade )
22

23
return U;

24

4.1.6 The ? : Operator

is the general structure ofthe ?: operator.

Exp1? Exp2: Exp3
determined like this:
The value of a ? expression is
of
is evaluated and beconmes the value
evaluated. If it is true, then Exp2
. Expl is
the entire ? expression.
and its value becomes the value of the
then Exp3 is evaluated
lf Expl is false,
expression.
4.2 Looping Structure
allow for more compli-
various control structures that
Programming languages provide statement or group
allows us to execute a
A statement
cated execution paths. loop the following types
of
times.C programming language provides
of statements multiple
loops to handle ooping requirements.

while loop
do while loop

for loop

4.2.1 while loop

as a
executes a target statement as long
A while loop in C programming repeatedly
given condition is true.

while( condition )

statement(s)
The condition
statement or a block of statements.
be a single
Here, statement(s) may The loop iterates while
the
value.
and true is any n o n z e r o

may be any expression, false, the program

control passes to
becomes
condition is true. When the condition while loop
point to note is that a
the loop.Here, the key
the line immediately following tested and the result is false.
the loop
all. When the condition is
might not execute at after the while loop will be executed. flow
will be and the first statement
skipped
body
chart and progranm remaining

while( condition )

conditional code

condition

If condition
is true

code block Ifcondition

is talse

7: wliile loop flowchart

Figure

21
 4.2.2 for loop
A Or lo0p 1s a repetition control structure that allows you to efficiently write a 100p

that needs to execute a specific number of times.

for ( init; condition; increment ) i
2 statement (s );
3

h e i i t step is executed first, and only once. This step allows you to declare and
1itialize any loop control variables. You are not required to put a statement here,
as
long as a semicolon appears.
2. Next, the condition is evaluated. If it is true, the body of the loop is executed. lf
it is false, the body of the loop does not execute and the flow of control jumps to
the next statement just after the for loop.

3. Next, the condition is evaluated. If it is true, the body of the loop is executed. If
it is false, the body of the loop does not execute and the fow of control jumps to
the next statement just after the 'for loop.
4. The condition is now evaluated again. If it is true, the loop executes and the
process repeats itself (body of loop, then increment step, and then again condition).
After the condition becomes false, the 'for' loop terminates.

for init; condition; increment)

Conditional code

Init

conditlon

If condition
is true

code block Ifcondition

is false

increment

flowchart
Figure 8: for loop

4.2.3 do while loop

the of l e loop. tlhe
condition at top
wlich test the oop the loop.A
Unlike for and wl1ile loops, condition at the bottom of
checks its
in C programming
clo..while loop
25
 wlhile the lact that it is guaranteed to execute
do... wlhile loop is sinilar to a loop, except
at least one time.
do
statement(s);
}while ( condition );
Notice that the conditional expression appears at the end of the loop, so the statements)
in the loop executes once before the condition is tested.If the condition is true, the floww
of control jumps back up to do, and the statement (s) in the loop executes again. This
process repeats until the given condition becomes false.

do (
conditional code
}while (condition)

code block

f condition
is true

condition

If condition
s false

Figure 9: do..while loop flowchart

4.2.4 nested loop

C programming allows to use one loop inside another loop.

Nested for loop

for ( init: condition; increment ) {
for i n i t ; couditio increment )
statement (s ):

statement (s);

. Nested while loop

while (condition)

while (condition)
statement (s )

statemeint(s):

.Nested do wlhile loop

26
 do

statement (s)

do

statement (s);
while ( condition
9while condition ):
Find Prime numbers between 2 to 100 using prime number

#include <stdio .h>

int main () {
local variable definition */
int i J
for(i = 2: i<100: i++){
for (j 2; i <= (i/j ): j++)
=

if((iZj)) break; // if factor found, not prime

ifj>(i/j)) printf("%dis -prime\n", i);
10 return 0;
11

4.3 Break Continue and Goto Statement

4.3.1 Break Statement

The break statement terminates the loop (for, while and do..while loop) immediately
when it is encountered. The break statement is used with decision
making statement
such as if...else. The syntax of the statement is
break;
Example of Goto Statement

Enter loop

False
testexpression
of loop

True

Yes
break?

No
Exit Loop

Remaining body
of loop

Figure 10: Flowchart Break Statement

 10 nunbeTS
to calculate the sun of marunum oJ
Progrann
sum un til user enteTs poSilive ubeT
Calculales
2

3 # <st dio .h>

include
int main ()

6 int 1
double number, sum = 0.0:

for (i=l; 1 <= 10; ++i)

10 printfEter~a~n%d:" ,i):
11SCantf(%lf,knumber );
12 J user enlerS negalave num ber, loop 1s Lermi n aled
13 i f (num ber < 0.0)
14

15 break;
16
17S u n + = n u n b e r ; / / sum= sun1 + UUnber

19 printf'Sum=%.21f ,sum):
20 return 0;
21

Working of Break Statement

while (test Expression)

odes
if (condition for break)

break;

for (init, condition, update)

if (condition for break)

break;

Figure 11: Working of Break Statement

4.3.2 Continue Statement

Tlhe contime st at.ement skips soii1e statenlems isi(le the loop. The continue stateuent
is sed with decision making statement sucdh as if..else. The syutax is
continue;
 Example of Continue Statement

Enter loop

False
testexpression
of loop

True

Yes
continue?

No
EXit Loop

Remaining body
floop

Figure 12: Flowchart Continue Statement

numbers
/Program to calculate sum of marimum of 10
2// Ne.galive numbeTs are skipp ed Jrom calculalt0
3include <stdio.h>
i n t main ()

6 lnt i;
= 0.0:
double number, sum

i <= 10; ++i)

for ( i =1;
9

10 printf(Enteruand:,i):

11 SCanf(*%1f*,knumber ); is terminated
enters negative number, l0 0p
1 2 / 1 J user
13 i f (umber <0.0)
14
15 Continue;

sum SUmm UmbeT;

17 SUin t= nunber; //

19
printf("Sium.=%.21r" , sum ) :
20 return 0:

21
Statement
Continue
Working of
 while (test Expression)

if (condition for continue)

continue
}
Codes

for (init, condition, update)

if (condition for continue)

continue;

codes

Figure 13: Working of Continue Statement

4.3.3 Goto Statement

The goto statement is used to alter the normal sequence of a C program. The syntax
of goto statement is

goto label;

5label:
6 statements;

Example of Goto Statement

/ / Progr am to calculate the sum and average of marimun of 5 nunbers

2# include <stdio.h>
3 int nmain ()

5 Const int naxlnput = 5

6int
7 double number, average, sum=0.0;
for(i=l; i<=maxlnput: +i)

10 p r i n t f l . Euter-a -)umber: - i);

l sCanf("%If,kunber ) ;
1 2 / I f user enlers 7egative number, Jlow of program mones to label jump
13 i f (mber <0.0)
1 goto jump:
Sun l l ber, // Sum s u m t n u m b e r

16

17 JunP:

i Velape=sun/i - ):
1print Su11 .2T\n", suln);
300
20 printt(Average=-%.2f"|
average );
21 return 0;
22

Reasons to avoid using goto statement

. T h e use of goto statement may lead to code that is buggy and hard to tollow.

2. Goto make it is difficult to

junps that are out of scope so follow
 5 Arrays and Strings
Arrays a kind of data structure that can store a fixed-size sequential collection of ele-
ments of the same type. An array is used to store a collection of data, but it is often more
iseful to think of an array as a collection of variables of the same type.Instead of declar-
ng individual variables, such as umber0, number1, ..., and number99, you declare one
array variable such as numbers and use numbers|0, numbers|1), and ... numbers|99 to
Tepresent individual variables. A specific element in an array is accessed by an index.All
arrays consist of contiguous memory locations. The lowest address corresponds to the
first element and the highest address to the last element.

First Element Last Element

Numbers[0] |Numbers[1]| Numbers[2] Numbers3

Figure 14: Arrays Representation

5.1 One Dimensional Array

5.1.1 Declaring and Initialising

data-t ype array-name| array-sizc ];

double balance |10):
balance is a variable array which is sufficient to hold up to 10 double numbers.size of
array defines the number of elements in an array. Each element of an array can be
accessed and used as per the need of the program.
int age [5]={2,4 ,34 ,3,4};
int agell={4,6,8,9,10};

In the second case the compiler determines the size of an array by calculating the number
of elements in an array.

agel0) age[1J , agei2) age[3) age[4]

2
31

Figure 15: Arrays Initialisation

Program to find sum of marks of n students

#include <stdio.h>
int main ( ){
int marks | 10],i ,n,sum=0;
printf (Enterunumber-of-st udents:"):
scanf("d, kn);
for(i 0: i <n:+ + i){
printfEntermarksofstudent%d:,i+1)
scanf("A,kmarks| i });
siumt=narks | i|
print Sum/d ,sum);
12 return 0;
13

32
 5.2 MultiDimensional Array
programming language allows programmer to create
tidimensional arrays. arrays of arrays known as mul-

float a |2]|6]:

col l 2 col cet 4 ol 5 col 6

rowlOlo) »{0t1) a[0ji21|10]121 o1014) a10|15

2 a l 1 ]|O] ai 1 H1} al 112)|al 1)W3] al 1 ]|4 al 1}| 351

9 Muit diensionói À a y

Figure 16: Arrays Initialisation

5.2.1 Initialisation of Multidimensional Arrayss

int c{2][3] ={{1,3,0},{ -1,5,9}}
2 int c [2][3] ={1,3,0, -1 ,5,9;
In the second case the compiler creates two rows from the given array.
Program to add two matrices
#include <stdio .h>
2 int main (){
float a 2]|2], b[2]|2), cl2]|2];
int i , j
printfEntertheelementsof.lst-matrix\n" );

for ( i =0;i <2;++i) s

for (j =0;j <2;++j ){
printf( Enter-a%d%d: ", i+1,j +1);
scanf("%f*,&a|iJ[j)):

3 printfEnter the_elements.of~2nd~ matrix \n");

14 for (i =0:i <2;++i)
15 for (j =0;j <2;++j){
16 printf( Enter-b%A%d: ~" i+1,j+1); ,

17 scanf("%f*,&b[i]|i]):
18

19

20 for (i =0; i <2:++i)

21
for (j =0;j <2;++j){
22 clilli]=a|i][il+b[i]l[ij:
23
printf( \nSum-Of.Matrix :");
25
for(i =0;i <2;++i)
26
for (j =0;j <2;++j){
printf(Z.1f\t",c[i][i]):
27

28
if (j==l1)
printf(n"):
2"

30

31 return 0;

32

matrices
Program to Multiply Two
#include <stdio . h>
33
 i nt ain)

int, n , d, k, sum=0;
int first|10]|10] Second10)|10], multiply |10][I0];
printtmteTroWs.andcolumnsof.first ~mat riX \n
scanf"d7d , n, kn):
printiEnter -theuelements of-first-matrix \n
for (c =
0: c<1; c+)
for (d = 0; d < n: d++)
scanf( "%d", k first |c|d)
15
pTlnti EnterrOWSand.columnsofusecond-matrix \n
16
scanf("7d7d", kp, kqD
1s if (n= p)
19 printt can tbe-multiplied -with ~eaclh -other.\n):
20 elIsc

22 printi Enter-theelements~ofsecond matrix \n):

for (c =
0; c<p: C++)
25 for (d =
0; d < q: d++)
scanf(d" , &secondc}ldj):
2

for (c = 0: c<; C++)

for (d =
0: d<q: d++) {
30 for (k = 0; k < p: k++) {
3 sum= in + first c | k ] *s e c o n d [k} d]:

3
34 nultiply [c]|d] = sum;
Sum= 0;

39 print Productol -entered matrices:=\n)

for (c = 0; c<; c++) {
for (d = 0; d < q; d++)
3 printf("%d\t", multiply [e][d])

printf("\u):|
7

19 return 0:

5.3 String
Strings ale actnally one-dinensi0nal array of clharacters terminated by a uull character.
Thus a ull-teminated string contains the characters that comprise the string followed
by a ull.The followiug derlaration and initialization ereate a string consist ing of tl
word "Hllo". To lod tlhe nll character at the eud of tlhe array, the size of the charaeter
array coutaining tie stri 1s o I1ore tha the number of clharactes in the word

Hll

31
 char greeting 6|=" Hello"
char
greeting 16]={ 'I', 'e' , '1','T , 'o, \0

Index

Variable H

Address
Ow23451Ox23452 x23453x23454 x2345s 023455

Figure 17: String Representation

5.3.1 Accessing Strings

/ / n o meed to use address 8 in scanf for strings
2
Scanf"%s" , greeting);
3gets (greeting ):

5printf("%s" ,greeting ):
6piuts(8reetig):
5.3.2 String related fuctions

strepy(s1,s2) copies string s2 into the string sl.

concatenates string s2 onto the end of string sl

strcat (s1,s2)
the length of string sl
strlen(s1) returns

strcmp(s1,s2) returns 0 if sl and s2 are the same, less than 0 if sl <s2 and greater
than 0 if sl>s2

and places it in sl
strrev(sl) reverses the string sl

35
 6 Function
6.1 Function Definition
A function is a group of statements that togetner perform a task. Every C progra
has at least one function, which is main(), and all the mOst trivial programs can defin
additional functions.A function declaration tells the compiler about a function's name.
return type, and parameters. A function definition provides the artual body of th
function.

function
6.2 Types of C
There are two types of C functions

Library Function
.UserDefined Function

6.2.1 Library Function

Library functions are the in-built finction in Cprogramming sy'stem.

main ()
printf ()
3 Scanf()
strepy ()
5 strcat ()
6strcmp()
are the examples of Library functions available in C.

6.3 User Defined Function

C allows programmer to define their own function according to their requirenent. These

known user-defined flunctions.

types of functions are as

Function Prototype(Declaration)
should be declared before they are used. These type
Every function in C programming
of declaration are also called function prototype. Function prototype gives compiler
information about function name, type of arguments to be passed and return type.

int add (int a, int b);

6.4 Defining a Function

is follows
The general form of a function definition in C programming language as

parameter list )
return_type function-name
2 body of the function

A function definition in C Programming consists of a function header and a function

body.Here are all parts of a function.

Return Type A function may return a valuc. The return-type is the data type
of the value the fnction returns. Soie functions perfom the desired operations
WIthhout Ieturning a value. n this case, tle returntype is the keyword vOl.

Function Name This is tle actual naue of the lunction. Tlhe lunction ane ad

e paralleter list together coustit ute the uiction Sigiatnre

36
 raraneters A parameter is like a placeholder. When a function is invoked, YOu
pass a value to the This value is referred to as actual parameter
O argunent.
paraneter.
The parameter list refers to the type, order, and number or e

PaLeters ol a tunction. Parameters

no parameters.
are optional: that is, a functio1 lay cou

nCton Body The fhunction body contains a collection of statements that deline
what the function does.

6.5 Calling a function

Function with return and without retuen can be called to using the different syntax.

add (a,b); //calling function wthout return

2
C=add(a,b); //calling function with return

6.6 Call by Value

If data is passed by value, the data is copied from the variable used in for example main()
to a variable used by the function. So if the data passed (that is stored in the function
variable) is modißed inside the function, the value is only changed in the variable used
inside the function.
1 #include <stdio .h>
2 void call.by-value (int x) {
)
printt("Tnside-funetion -x=_Xd-before -adding-10.|n",
x

X+= 10:
printf Inside.function -x_=_d-after ~adding-10.\n" x)
6

7 int main ( )
int a=10;

10
printf("a=_Tdubefore function .\n, a):
call-by-value (a);
12
printf(a=dlafter~function.\n", a);
13
return 0;

14

iformation at
In the main() we integer that has the value of 10. We print some
create a

printing our variable a. Then function call_by-value is called

every stage, beginning by
then copied to the function variable x.
and we input the variable a. This variable (a) is
Then when the
In the function we add 10 to x (and also call some print statements).
next statement is called in main() the value of variable a is printed. We can see that
the value of variable a isn't changed by the call of the function call.by_value().

6.7 Call by Reference

to the data is copicd instead of the actual

If data is passed by reterence, a pO1iter
is done in a call by value. Bccause a poiuter is copied, if the valuc at tlhat
variable as
in maiu().
address is clhanged i the fuiction, thc value is also clhangcd
pointers
#include <stdio .h>
2 void call-by-reference (int *v){
printf(" Insidefuneti0n -V=dbefore ~adding-10.\n", *y):
(*y)+ 10:
printfTnsidc~iunet101 -V-/daftcr-adding-10.

37
 b):
,

unetiOn.|

man int b 0:
inl
b e t o r e .

b);
Call.hv-relerence(ab)
P r n t t
..after.Iuuetio.I
h.
..

b.
Tntl

r e t u r n

10.
10.
The
function call. by.reference is
value
function
the
has to this
b
that passed there is 10 added to the vahe
integer
variable
b is done
and
with an
the
the valie is 20.
We start
address
of the
print
statement

Of
the
function
Then
and the
end
alter the an see the value is changed
alled before
a
anned
T ' h e r e f o r e
at
as you
can (as
byy.
some
there is b
and
pointed v a r i a b l e

the
memory the
print
t we ag
in main(0
expected) to 20. f u m c t i o n

to a
argument
funet
ction
an to the
as a r g u m e n t

array as an
Passing be passcd
O.6
can
array
floats an
int and
LIkewise

all.int
size
)
float
float
largest (
1.6,3.4,6.8
main ()1 (4]={2.5,
-

3
float value
largest
(value , 4 ));
Y\n°,
printf
s1ze)t
(float al|, int
float Targest
6

int i
float max;

max-a | 0 ;
i++):
=l:i<size;
for(i if(maxca i])
11
max=a| i;
return(max)

Class in C
6.9 Storage
6.9.1 auto
class for all local variables.
class is the default storage
The auto storage

int mount;
auto it month;

variables with in the samc storage class.

'auto can
o
The example above defines two

be used within fnetions. i.c.,

local variables.

6.9.2 register
class is used to define local variables that should be stored
The register storage the
register instead of RAMI. This means that the variable has a maximum size eq12a1 t
it (a
register size (usually one word) and can't have the unary '&' operator applie
it does not have a memory location).

register int iles

 The register should
ouly be used for variables that require quick access sucll
4s
unters.
It should also be noted that defining 'register' does not mean that the variabie
be stored m a register. It means that it MIGHT be stored in a register depenag

hardware and
implementation restrictions.
6.9.3 Static

ne static storage class instructs the compiler to keepa local variable in existence aurE
the nie-time of the program instead of creating and destroying it each time it comes
and goes out of scope. Therefore, making local variables static allows them to mainti
es between function calls. The static modifier may also be applied to globa
to the nie
varldles. When this is done, it that variable's scope to be restricted
causes
member,
WC t 1s declared.In C programming, when static is used on a class data
causes only one copy of that member to be shared by all the objects of its class

#include <stdio.h>
2 void func (void );
3 static int cont = ; /* global rariable +/
main()
while (count--)
func ();

return 0;

10 u n clion definition */
11void func( void) {
12
static int i = 5: /* local static variable */

1++
printf"iuis%d.and-count -is d \n", i , count)
14

15

6.9.4 extern
a reference of a global
variable that is visible
The extern storage class is used to give
When 'extern', the variable cannot be initialized
to ALL the progran files. you use

variable uame at a storage location that

has been previously
however, it points the
define a global variable or function,
which
defined. When you have multiple files and you
then extem will be used in another file to provide the
will also be used in other files,
extern is used to declare
reference of defined variable or fhunction. Just for understanding,
a global variable or function in another file.

6.10 Recursion
recursive function technique and this is known as
A function that calls itself is known as
is more elegant and requires few variables
which
recursion in C programming.Recursion
make program clean. Recursio1n can be used to replace complex nesting code by dividing
of its sub-type.In other hand, it is hard to think the
the problem into same problem
function. It is also diffhcult to debug the
code containing recursion.
logic of a recursive

Factorial Using Recursion

6.10.1

1#include<stdio .h>
2 int factorial (int n);
3 int nain ()
 int n
Pnt Enter..an-positiveinteger )
scanf( d",kn):
int("Factorial.ofYd=%ld" , , a c t o r ial(n)):
return 0:

11int actorial (int n)

13 i f(n'= 1)
4
retur n* fac torial (n-1);

Recursion
6.10.2 Fibonacci Series Using

#include<stdio.h>
int Fibonacci (int ):
31ai )
int n, i = 0. c:

scanf("%d ,kn):
printf Fibonacci~series \n);
Ior C =1 C<= n ; C++)

printf%d\n, Fibonacci (i)):

12

13 return 0;
14

15 int Fibonacci (int n)

6

if n=
return 0:
clse if n = 1 )
0
retur 1:
21 else
2 return Fibonacci (n-1) + Fibonacci (n-2) ):
23

6.11 Preprocessor Directives

Belore a C program is coipiled in à compiler, source code is processed by a progra
called pieprocessoI. This process is called preprocessing.Commands used in preproe
are called preprocessor directives and tlhey begin with "#" syubol.
#include<stdio.h>
#define height 100
#define number 3.14
#define letter A
#define letter-sequence "ABC"
#define backslash-char ?'
void main (

printf valuC of -height: d\n , height );

print valueof -number: %I\n" ,number);
printfvalne ofletter~:c \n° ,letter)
printfvalue -ofletter-sequence : 7s\",let ter-sequeu
printtvalue ofbackslah-char~: c\n" ,backslash-c th at '
getch

40
 Preprocessor Syntax Description
Macro # define macro defines con-

stant value and can

be any of the basic

data types
Header Iiclusion#include<file-name>| sourcecode of the file
Files included
filename is
in the program at the

specified place
are
Conditional Conpi- #ifedt, #en-set of commands
included or excluded
lation dif, #if,#clse
in source program
before compilation
with respect to tlhe

condition
#undef is used
Other directives #ndef, #pragma to undefine a de-
macro vari-
fined
1s
able.#pragina
used to call a func-
tion before and
after fnction in C
program.

Table 2: Preprocessor Directives

6.12 Macro Substitution

One of the major use of the preprocessor directives is the creation of macros. Macro
Substitution is a process where an identifier in a program is replaced by a predefined
form of macro definition is
string composed of one or more tokens.'The general

#define identifier-s tring

2 #define count 100
3 #define area 5*12.46
4#define cube (x) (x *X*x)
 name
flow File Description
process
Program in each steps

sample.c
/macro,
Sourcecode replaces
#define
Preprocessor
conditional
compilation
#include (files), their
Preprocessor
#ifdef,
#ifndef by file
codes like codes in source
values & source

Respective

sample.i
Expanded source code source code
expanded
- Compiler compiles
s o u r c e code

Compiler to assembly

sample.s
Assembly source codej that
converts assembly
program
It is a code to object
code.
ASsembler SOurce

sample.o
Object code that
object code
converts

T h i s is a program combines all

code and also
executable
to
object codes together.
Linker
sample.exe
Executable codej in CPLU and
-Executable code is loaded
loader program.
Loader executed by

Execution
Compilation
Figure 18: C
program

7 Pointer address
another variable, i.e., direct
the address of before
variable whose value is declare a pointer
must
A pointer is a
variable or
constant. you declaration
location. Like any variable
of the memory form of a pointer
The general
variable address.
to store any
using it
S

Var-lalme ; var-name i1s

*
type and
must be a valid C data type
is the pointer's base type: it declare a pointer is the s a m e
Here, type asterisk
*
used to
variable. The used to
the n a m e of the pointer the asterisk is being
However, in this s t a t e m e n t declarati101s
multiplication.
asterisk used for of the valid pointer
Take a look at s o m e
as a pointer.
variable
a
designate
lo0 an 1n ieger */
int *ip /* po1nler
to a double */
2 double *dp; /* pointer
pointer to a float */
3 float fp; / character */
pointer lo a
char *Ch /*

Using Pointers
7.1
#include <stdio . h>
i n t main ()
/* actual var7able declaralron *
Var= 20;
int
*/
int * 1P /* p01nler v araable decl(aratio
store address of var n pointer tartable */
ID=&Val; /*
12
 printiAddress of_varvariable: -%x \n, var
/* 001aress sloTed in pointer variable */
10 Printi Address.ustored -in ip-variable: %x \n ip
/acces$ the value using the poinler
prntt
*/
12

13
Valueofuip~variable : Id \n", *ip )
14 return 0;
15

7.2 Null Pointer

yon
do

aiways good practice to assien a NULL value to a pointer

a
variabie la
of variade
not nave an exact address to be assigned. This is donc at the time

A pointer that is assigned NULL is called a null pointer.

#include <stdio.h>
int main () 1

int *ptr = NULL;

PrInti The-value-of-ptr.is~: Ax\n, ptr

return 0:

7.3 Pointer Arithmetic

can perorm
Thercfore, you
numeric value.
p o n t e r in address, which is
c is an
a
There are roiur
can on a
numeric value.
operations on a pointer just you
as
altnmetc

be used on pointers: +t, , t, and

-
arithmetic operators that can

ptr++ 1004 because caclh

time
to the location
the above operation, the ptr will point next to
Alter
location wlhich is 2 bytes
to the next integer
ptr is incremented, it will point m o v e the pointer
to the next
16 bit system. This operation will
the current locatioin in location. If ptr
valuc at the memory
the actual
location wit hout iupacting will point to the
meniory above operation
character whose address is 1000, theu the
points to a
next character will be available at 1001
location 1001 because the

7.3.1 Incrementing Pointer

the variable pointer
instead of array because
an

We prefer using a pointer in our progranm

incremented because it is
a
name which cannot be
the array
can be incremented, unlike
constant pointer.
#include <stdio .h>
2 int main () 1

int var
|3 =
{10, 100, 200}
int i, *ptr;

addTess 7n pol7N teT */

ariaY
/* et uS a ve
ptr Var:

i 0: i < 3: i++){
for ( =

i, ptr ):
Addressof-var|%d)-=-%x\n,
printf(" I, p t r );
printf("Value-ol-var|%d] =al\
2 location */
/* moUe lo the 11ext
ptr++
15
retur 0;

17

Decrenenting a Pointer

ter variable c
can decremon
a n also be decremented wliich
7.3.2 variaDie

the poiiter
increment of pointer
Likewise the

shown as
include <st dio . h>
nmain ()
2 int
3 100, 200:
var|3
=
{10,
int
int i, *plr 1.n O1n
teT */
a ddresS
have array
e us
/*
ptr = kvar |2]
i--) 1 ptr ): i,
i 2; i >= 0;
for printf("Address-ofuvar
=
[%d)=_%x \n"
i, * ptr );
[%d]=%d\n,
intf("Value-of-var
locatro n */
noUe to the previous
/*
ptr-

return 0;

15

Definition Pointer
to Arrays
7.4 of the array. Therefore, in the
element
to the first
An array name is à const ant pointer
declaration
double balance | 50|;
address of the first element of tlie arrar
is the
balance is a pointer to
&balance|0|, which as the address
of the first
assigns p
progran1 fragnent
balance. Thus, the following
clement of balance.

Idouble *p:
2 double balance | 10]
=balance : //p=sbalance
[0;
3p
v e r s a . Therefore, *(balance
names as
constant pointers. and vice
It is legal to use array
you store the address
the data at balancel4|.Once
+4) is a legitimate way of accessing using *p. *(p+1), (p2)
can access the array elements
of the first element
in 'p, you

a n d so 0n.

#include <st dio . h>

i n t nmain ()
3

/* an array u'ilh 5 elements */

{1000.0, 2.0, 3.4, 17.0, 50.0);
balance |5
=

5 double
double *p
int
P=balance; //p=balance (0

0ulput each array ele ment 's value /

/*
11 printf"Array-Values- us n8-pointer \n"):
f o r i = 0; i< 5: i + )
printi (p-tl) :%f\n i , ( P + i));
14
 PTINt Arayalues-usingbalaneeaSaddess \
for i
:
PTintt i(balanee t«l):.
itt "):
return 0 alance ta)
%t\" i
(balancet
main({
2
int *p,
sun, i; ,3}
int x5}={5,9,6,7
i=0:
5
P-X //p=8r 0
while(i<5){
printf(" x|%d| _%d
Sumsum+*p " ,i
,*p,p)
12

13

e e une
printt\nsnn=%d\n ,sm );
base
e nt
address of array
x is
poiited by the
pointer
assigned to the pointer p. sum adds e he value
ncreases the value p using (*p)
ndirection of
of the operator and the inerene
he address variable i by i and the
the sum is pointed by p which is an integer and inerement p++ increase tn vvalue of
caleulated and printed.
infact increased 2 by
bytes.Uitimae
7.5
Returning Multiple Values from
Return
a
function
from
statement can return
single value. however
a
mnctions
using arguments that we multiple values can be returnea
1Sed to send out pass to a funetion.The
information are called ontput arguments that are
through arguments is achicvedparameters.
back information The mechanism of sending
operator (&) and indirection operator (*). using what arc known as the address
void
2 main (O{
mathoperation (int x,int y,int *s
, int *d);
int x=20.y=20,s ,d:
mathoperation (x ,¥,&s,&d)
printf(" sum-7d\n.diff=d" ,s ,d);
}
void mathoperation (int a, int b, int *sum, int
*Sum=a+b; diff){
* diff=a-b:

The variables *sum and *diff are known as

pointers ad sum and dift as pointer vari-
ables.Since they are declared as the int, they can point to locatious of int
type data.
7.6 Pointer to String

As string can be cOisilerCd as a cliaracter àlray. C supports all

altemat ive war toe
CTCate
strings Usiug poiuter variables of type char.
char *Str 80od
 This creates a string literal and then stores ls aldress in the pointer variables str. Tlhe
pointer now pointer to the irst character or tlc Selng good.we can print the content

the str using printf or puts function tent of

print f("%s* , str);

2 puts( s t r ) ;

Remember although str is a pointer

string8, to the it is also the name of
the stringG
Therefore we do not need an indirection operator *.

1main(){
2 char *nane:
3 int lengt.h:
4 char *cptr=name;
5 name="DELHI"

6 printf"%s \n" ,name);

while (*cptr!= '\0){
printf C i s stored~at ~address ~at _fu\n" ,*cptr ,cptr ):
cptr++
10

11length=cptr-name;
12 printf°\nm-Length of-String-is = d \ n name)
13

7.7 Double pointer

Stores the address of a pointer variable. Generally declared as

** ptr;
#include<st dio .h>
int main ()

int num =1 5 *ptr **ptr2ptr

= daun;
ptr
7 ptr2ptr = &ptr;

printf("%d" , ** ptr2ptr )
return ( 0);
10

7.8 Dynamic Memory Allocation

The exact size of array is unknown untill the compile time,i.e., time when a compier
compiles code written in a programming language into a executable form. The size of
array you have declared initially can be sometimes insufficient and sometimes more than
required. Dynamic memory allocation allows a program to obtain more memory spaec,
while running or to release space when no space is reqnired.

7.8.1 Malloc

The name malloc stands for "memory allocation". The function malloc() reserves a
block of memory of specified size and return a pointer of type void which can be casted
into pointer of any form

ptr=(cast-1ype *) malloc( byteS1ze)

46
 Fnnction Use of Function
malloc OcateS requcsted size of bytes and returis

calloc pointerfirst byte of allocated space

locates space for au array clements, initianze>
tozero and then returns a pointer tone
iree
cdellocate the previously allocated space
realloc LChange the size of previously allocated space

able 3: unction Dynamic Memory Allocation

nere, ptr 1s pointer of cast-type. The malloc() function returns a pointer to an aea of

memory with size of byte size. IfIt allocation fails and retul
S17e. the space
the insufficient,
space is insutficient, &id
NULL pointer yc
ptr=(int*) malloc (100»sizcof (int )):
is statemeut will allocate either 200 or 400 according to size of int 2 or

TEspectively and the pointer points to the address of first byte ot

memoy
7.8.2 Calloc

The nanie calloc stands for "contiguous allocation". The only difference betweeu
C u i d calloc() is that, malloc() allocates single block of memory whereas cailoc
allocates nultiple blocks of meniory each of sane size and sets all bytes to zerd.

ptr=( cast-type *) calloc (n, element -size);

This statement will allocate contiguous space in memory for an array of n elemet

ptr=(float ) calloc (25,sizeof (float )

This statement allocates contiguous space in memory for an array of 25 elements eacn

of size of float, i.e, 4 bytes.

7.8.3 free
does not get return on
Dynamically allocated memory with either calloc() or malloc()
its own. The programmer must use free() explicitly to release space.

free (ptr);
statement canse the space in memory pointer by ptr to be deallocatcd.
This
Find sum of n elements entered using malloc

#include <stdio.l>
2 #include <stdlib.h>
3 int main ()1
nt n,l ,* ptr , sum=0:
p r i n t "Enter~numberof.elements:"
scanf("Yd" ,&n );
//1malloc allocation
ptr=(it *) malloc (*sizeof(int));
if(ptr=NULL)

printt("Error! nemory-not-allocated. )
Cxit (0):

printlEnterelemenisuolarray:

=);i<u:+++1)
14 for ( i
16
Scanf(%a" , ptr+i)
18
Sum+=*(ptr+i):
I9
printf (" Sum-%d" ,sum);
20

2
free(ptr)
return 0
22

Fnd sum of n elements entered using malloc

#include <stdio.h>
2
#include <stdlib .h>
a int main
(){|
int n, i ,* ptr ,sum=0;
printfEnterunumberofelements:~")
scanf(7d" ,kn);
ptr=(int ») calloc (n, sizeof (int));
if(ptr=NULL)
printfError ! nemorynot -allocated. ):
exit (0)
2

13

14 rintfEnteruelements-ofuarray:):
for(i =0;i<n:++i)
15
{
scanf(7d" , ptr+i);
18
sumt=*(ptr+i ):
19
printf( Sum=%d" ,sum);
20
free (ptr);
21 return 0:
2

A8
8 Structure and Unions
A structure is a
collection of logically related data ler a
items
Singie name, callecd structuretag The data itens enclosed within a structure are known
grouped togeie
as members. The members be of
can same or different data types.
struct structure_name

data.type memberl
datatype member2;
data-type member3:

Examples of Structure can be as follows

struct employee
int emp_id;
char name |25
int age;
float salary:

7el, e2
witl
are associated
a structure do not occupy memory until they
Tne
members of
SUructure variable. Above examples shows the structure
variable el and e2 of structure

employee.

8.1 Accessing Members of Structure

help of .(dot) operator.

The syntax
The members of a structure can be accessed with the
follows
for accessing the members of the structure variable is as

struct-variable .member
2 struct employee el
3 el.emp-id;
4 el.name
5 el.salary

8.2 Initialising Structure

in the definition
the structure must appear in the order as
The valucs to the members of
and separated the by commas. C does not allow the
of the structure within braces
from
of individual structure
members as within the definitiou. The general
initialisation
is
struct-namevariable={value.l , value_2 .
. . . .

, value-n};
2 struct employee

int cmp-id
char name |25:
int age
float salary;

9
,25,80000.0}
10 struct employee el={555,"Sudip
are initialised to 555, "Sudip",25,80000.0
variable el empd,name,age,salary
The members of the
 Array of Structure
8.3 structure
can be initialised.
of
arrays
data types
LIkewise the array of

I#include<st dio . h>

2#include<conio.h>
3struct employee{
int emp-id :

char name | 25j

int age ;

float salary

9 int main ()
10
struct employ ee el50:

12
int i n;
for ( i =0; i <50:i++)

-and-Salary
-name, -age age,&e [i ]. salar
p r i n t f E n t e r - i d ,
elil.1name,vel1|.
fi ]. emp_id,
b scanf(%%s%d%f",&e
<50: i++){
18 for ( i =0;iprintfDataon-Employec_%d" ,i +1):
printf(ID:%d,elij. emp_id );
20
,e[ ij.name);
printf"Name:%s"

21 printfAge:%d ,elij. age);

2 ,elij. salary );
printf( Salary:%f"

getch ( )

8.4 Nested Structure

the case tlhe
needs to have multiple values, For
the menmber of
structure
Sometiines
s t r u c t u r e type.C
allows the member
variable of another
members should be another of the structure. Nesting
The nechanismn is called nesting
structure to be the
s t r u c t u e . structure
illustration of nested
data structures.Following is a n
enables to build powerful

struct date{(
int day , month , year;

3
4 Struct employee{
int emp-id
char name |25]:
struct date dob;

struct employee{
int ep-id;
char name | 2 55:
struct datet
int day;
int month
int year;
} dob

Accessimg the mcmbers of the neCsted structure

50
 ##includecstdlio.h>
#include<conio.h>
3struct employee
int en p-id:
char ame |25:
int age
float salary
struct date

10
int day;
int month:
12
int year;
13
dob:
14

15 int main ())

16

17 struct employee el50];

I8 int i,11:
for ( i =0; i <50: i++)
20

printi ("Enteruid, name, age ~and-salary):

21
[il.name,&e [il. age,&elil.
salary
)
22
Scant %sATf.&e [i].emp_id,e
23 printfEnterthe~date~of.birth" ): :
i ]. dob. year )
l%d°,ke[i). dob. day,ke [i].dob. month,&e [
SCani
25

26 for ( i =0;i <50; i++){

printf( Dataon.Employec7d",i+1):
printfID:%d°" ,elij.emp_id):
printfName:%s" ,c[|il.name);
printf ("Age:%d" ,e[i. age
printf [ i salary );
Salary :% f" ,e j.

printf(Date-of-Birth -isd-Zd-%a" ,e[i].dob.

year
33 ei].dob.month,e[i].dob.day):

getch (0:
36

8.5 Pointer to a structure

We can have a pointer that holds the address of the structure. We can declare a pointer

variable of a structure by writing

struct structname * pstructvar:
the name of the userdefined
where struct is the required keyword structname represents
the pointer variable.The address of the
structure and pstructvar represets the name of
variable to the pointer variable c a n be assigned
as
structure

pstr11etvar=kvaribale :
stricture variable c a n be arcessed and proceSsed as
Likewise the pointer to the
ield-naune=variable:

I(*Struct-uame ).

struct-uamie->ield-ianile=va'iable

#include<stdio.h>

2 struct emplovee

int enup-id
 char ane | 25:
int age
float salary:

9 int main ( ){ 25,80000.0}

={1,*Roshan,
struct employee el
struct employee * pstructvar,
pstructvar=kel;
);
printt("Data on Employee pstructvar->emp-id ):
printf(Emp-ID=%d" ,
printf("Name-s pstructvar->char):
printfAg=d ,pstructvar->age );
pstruetvar->salary
):
printf(Salary=%1 ,
17

8
getch ():
return 1;
19
20

Structure
8.6 Self Referential
structure v a r i a b l e
ot the same type.
point to a
have members which
A structure can widely used in dy-
referential structure.
It is
structure a r e called
self
These types of
is the syntax of the self referent ial
structure like linklist,
trees etc.Following
namic data
structure

struct struct-name

21 data-type memberl;

struct-name * next
struct

6
structure of its own type. The
of a pointer variable to point
The next refers to the name
another structure of
a member that points to
struct.name will contain
structure of type
type struct_name.

8.7 Union
differences.Declaration of the union is the
almost like structures with subtle
Union are
struct the keyword union is used.
s a m e as structure. Instead of the keyword

union union name

data.type mem berI;
data-type member2;

data type member3;:

Union
8.8 Difference between Structure and

2
 Structure
INeyword struct defiues Union
structure ReyWord union defines Unio
KeywOTu
struct 1ystructurel
Sttuct myun1on{
int id;
int id
char name |20 char name ( 20;
float age float age
sl
ul
a structure all member gets F o r a nion compiler allocates he

alloated of all
members have address memory for
that increase as
the largest e
the declarators are ber.
read left to
the
right.The total size of
struct ure is the sum of all the
members.
WIthin structure all members gets| While retrieviing data r o n a
a

Coryallocated; tlherefore any the typethat is being retrieved

cmber can be retricved at any be the type most recently storea:
time.
One or more members of structure
can be initialised at once.
A union may only beofinitialised
its first
WI me-
a value of the type
ber.

Table 4: Difference between structure and inion

9 File Handling in C
stored.
A Ie represents a sequence of bytes on the disk where a group of related data is
File is created for permanent storage of data. It is a ready made structure.In C language
we use a structure pointer of file type to declare a file
FILE fp

9.1 Opening a File in C

The fopen() function is used to create a new file or to open an existing ile.
1fp = FILE *fopen (const char *filename, const char *mode )
2 fp=fopen (" text.txt","w");
3//0pens a file text. t r t in writing mode

Here filename is the name of the file to be opened and mode specifies the purpose of
opening the file. *fp is the FILE pointer (FILE *fp), which will hold the reference to
the opened(or created) file.
File xPIY >Nu
9.2 Closing a File Ptrz o p n t
The fclose() function is used to close an already opened file.
1 int fclose ( FILE *fp );

Here felose() lnction closes thc file and returns zero on success. or EOF il tlhere is au
cror iu closing the tile. This EOF is a coust ant delied in the header file stdio.l1.

3
 7 p t s st
mode
description
opens a text file in rcading node
opens or crcate a text nle in writing mode

opena fhle m appeid mode

opens a file in both reading and writing mode
W opens a file im both rcading and writing mode
a+ opens a file in both reading and writing mode

Table 5: File opening modes

9.3 Writing Character by Character in File

In the above table we have discussed about various file
1/0 functions to perform reading
and writing on file. getc() and
pute() are simplest functions used to read and write
individual characters to a file
#include<st dio .h>
#include<conio .h>
31main(0
5 FILE *fp;

6char ch;
fp = fopen ( o n e . txt", w):

printf( Enterdala" ):
9 while ( (ch getchar ())
= != EOF) {
10
putc (ch , fp );
11

12 fclose ( fp );
13 fp = fopen("oue. t x t " , r " ) ;
14 while( (ch = gete ()) ! EOF)
15
printf("%¢" ,ch);
16 Iclose ( Ip );
17

9.4 Reading and Writing From a file using fprintf () and fscanf ()

1#include<st dio.h>
2 #include<couio .h>
3 Struct emp
4

5 char name | 10);

b int age
7

9 void main ()

struct emp e
2 FILE *p,*q
p fopen ("one. txt,"a):
= fopen (one. t x t , r ) ;
15
printf(Enter Name and .Age);
scanf("%s %d" ,e.name, ce. age ):
fprintf (p, "%s _ l . e.anne, e. age );
fclose (p):
19 do
 20

21

22
fscanf (q,"%s YA"
e.name, e.age)
printt("/%s d", c .name,
,

23
.age)
24
while( !feof (q) );
25
getch ();
26

s Program, we have create two FILE

nle but in
different modes. fprintf() pointers and both are refering to the same
readis from the file,
function directly writes into the file, while fscanf)
which can then be printed on console nsinf standard
printf() function.
9.5
fread() and fwrite()
fwrite ptr, int size int n, FILE *[p ):
The fwrite()
function takes four
ptr ptr is the reference of an arguments.
Size size is the
array or a structure stored in memory.
total number of
n : n is
bytes to be written.
number of times a record will be written.
FILE* : FILE* is a file where the records will be written in
binary mode.

#include<stdio .h>
2 struct Student

int rol1:
char name [25];
float marks;
7

s void main ()
9

0 FILE fp
char ch
struct Student Stu;
fp = fopen (" Student. dat" , "w" ):
14 do
printf (" \nEnter-Roll.:" )
16
scanf("%d" ,& Stu. roll):
17
printf ( EnteruName: )
18
scanf(%s" ,Stu . name);
19
printf Enter Marks:");
20
scanf("%f" ,&Stu . marks);
21
fwrite(&Stu , sizeof (Stu) ,1,fp)
22
printf( nDo-you-wanttouaddanother ~data-(y/n) :");
23 ch = get.che ( ):
24
while (ch='y' | | ch= Y'):
25 printf\nData-writt.en ~successfully ... "):
fclose ( fp );
27

fread( ptr, int size, int , FILE *fp ):

The fread() function takes four arguments.
ptr ptr is the reterence of an array or a structure where data will be stored after
reading.
size: size is the total number of bytes to be read from file.
n: n is number of times a record will be read
 FILE FILE* is a file wlhere records will be read.

#include<stdio.h>
2 struct Student

int rolT
char name |25:
float narks;
}:
8 Void main (){
FILEfpP:
10 char ch
struct Student Stu;
12
fp =fopen (* Student.dat,"r"):
T3 i f(fp == NULL)
14

15 prnti nCan topenfile -or.file doesn exisl.

exit (0);
17

18
printf("\n\tRoll\tName\tMarks\n" );
9
while (fread (&Stu , sizcof(Stu) ,1,fp)>0)
Stu. maTRS )
20
Printt(n\t%«d\ t%s \ \%f" , Stu. roll ,Stu.nane,
21

2
fclose (fp);
Write a program to write details of student to a file and read the same file a d display

the records.

#include<st dio .h>

2 struct student{
3 Char name |20;
4 int age
5 char dept |20;
6

7 int main (){

8 FILE *fp:
I p=lopen ("student. lxt,"w+);
0 int i
struct student s |2:
for (i =0;i <2; i++){
3 printf( Entername");
scanf("%s" , s |ij.nane);
5 printf( Enter-age");
scanf("%d",&s| i|. age );
printf(Enterdept" );
scanf%s" ,s|i . dept );
19 fwrite(&s[i],sizeof(s) ,l ,fp);
20

21 rewind(Ip );
for (i =0;i <2; i ++)}
23 fread(&s [i],sizeof (s),1, fp );
24 printf |1Nane: %s \tuAge: d \t Departnent: %s
25 si.name,s | i|.age , sij.dept );
2D

2 fclose (fp );
2 return 0;

2
 Write a
progrann to
input data of 100
employees living in enmployee to
to a file and records of thiose
display recor
"Kathmandu"
#include<stdio .h>
#include<string .h>
3 struct employeet

char name |20}

char address |20];
long telephone
float salary :
struct dob{
int mnm, dd , yy
db
2

13 int
main (){
14
struct cmplovce
15 int i:
c
|100]:
16 FILE fp;
17
fp=fopen ( employee. txt", "w");
18for (int i= 0; <100;
19
++i)
20
printi nnter -nanne ):
scanf , i]. name)
printf|nEnter~address"
scanf(%s" ,c|il. address ):
):
printf nEnter.telephone" )
scanf(%ld" ,&e[ij.telephone ):
2 printf\nEnter~salary);
scanf ("%f" ,ke[ i]. salary );
printf nEnter~date -of.birt h -in dd-mn=yyyy" )
29
scanf( d-d-7d" ,ke [i]. db.dd,&e [i].db .mn&e|ij.db. YY)
31 fwrite(&e|il,sizeof(e) ,1,fp);
32 for (int i =
0; i < 100: ++i)
33

4
if (strcmp ("Kathmandu
{ ,eli].address)==0)
3b
37 printf(n%s" ,elij.name);
38
printfn%s" ,e[ij. address );
printf(\n%ld" ,e[ij.telephone):
40
printf(u%f" ,eli]. salary );
printf(\n'%d-al-%d" ,e[i]. db.dd,e[i].db.mm, e [ i ]. db.
12
yy):
43 return 0;
44

Write a program to read the name, anthor and

file library.dat.. Now print t he book name and
price of 500 books in a library from the
300.
price of those books whose price is above

#include <stdio .h>

#include <striug .h>
3struct book
char name |100
char author 100
float price;
 int main )

FILE fp:
struct book b:
Tp=fopen ("library.dat." ,"r"):
3

while ( fread (&b, sizeof (b) , 1 , fp)>0D){

5 if (b. price >300.0)

printf "%s \n" ,b. name);

I8
printfCAf\n" ,b. pricc);
20

21
22 return 0;
23

Write a program to create a 'student.txt" file to store the above records for 100 Stue
Also display the records of st udents who are not from Pokhara.

#include <stdio.h>
2 #include <string.h>
3 struct student
4

int roll
char name |20|
char address |20;
char faculty (20:
struct dob

int mm, dd, yy

2 db:
13

14 int main ()
5

FILE fp;
int i;
struct studcnt s [100)
fp=fopen (" student . txt" , "w* );
for (int i = 0: i <100; +i)
21

21

22
printf( EnteruRoll No. \n" ):
23
scanf("Ya ,&s|i]. roll);
24 printi(nEnter~name" );
scanf'"%s" ,s|ij.name);
20 printf nEnter-address" ) :

2 scauf(%s,s|i . address );
printf nEnter-Facult y" ):
scanf("%s" ,s[i. [aculiy );
printf (" \nEnter~dale~of.birth-in -format ddmm-yyyy" )
scanf("Zd-Zd-%a" ,ks [ij.db.dd,&s |ij.db.mk s[i.db.vy );
fwrite(&cs | i , sizeof(s),1,fp);
3
for (int i = 0: i < 100; ++i)

if(strcnp("Pokhara",siaddress)!=0)

printf I\u,s | i . roll ):

DrintCs\n",si.1alne):
40 printf("%s \n", s [i]. address );
4
printf("%s \n" , s|i]. faculty );
2 printf("d-%d-d \n",s [i ].db.dd,s [i].db.mmm,s [ i).db. yy ):

43

44

45
fclose (fp);
46
return 0;
47
prin tF C FZLE
Tta,

FZLE *f2
= fa0en c tie na- ode"))
 Contributed By

Abdul K. Khan & Jaya Paudel

BScNotes Contributors from Amrit Science Campus